How to Interpret a Solids Flow Report
By Joseph Marinelli, Solids Handling Technologies, Inc.
In order to determine if a new bin or silo will work reliably or to be able to make modifications to an existing troublesome bin or silo, you could use this guy or you could measure your solids flow properties. To begin this process, you need to know: what type of flow pattern can develop (modes of flow) and your material’s flow properties.
Modes of Flow
There are two modes of flow that can develop in a bin or silo, funnel flow and mass flow (expanded flow is another but is simply a combination of a mass flow pattern and a funnel flow pattern).
Funnel flow occurs because the hopper is not sufficiently steep and smooth enough to ensure sliding along its walls. In funnel flow, material flows toward the outlet through a channel that forms within stagnant material caused by friction on the shallow and/or rough walls. With a cohesive solid, this channel expands upward from approximately the hopper outlet, potentially to silo cylinder walls Even if the outlet is fully live, the preferential flow channel may empty out and form a stable rathole. This may:
limit your live capacity
cause materials to agglomerate or spontaneously ignite
cause powders to flood or flow uncontrolled
enhance particle segregation
cause silo failure.
Generally, a funnel flow pattern is only suitable for coarse, free-flowing, non-degrading solids when segregation is unimportant.
In mass flow, the hopper is steep and smooth enough to ensure flow of all the material whenever any solid is withdrawn, thereby overcoming the friction that develops between the material and the hopper wall surface. Where there are many disadvantages to funnel flow, mass flow has certain advantages, as follows:
flow is uniform
pressures acting at the outlet are practically independent of the head of solid in the bin
segregation of particles is minimized by the first-in- first-out flow sequence associated with mass flow and segregated particles are re-mixed as they discharge from the outlet
fine powders tend to deaerate and flooding is avoided, due to increased residence time
Generally, a mass flow pattern is recommended when handling cohesive materials, powders that can flood, materials which degrade with time and when segregation needs to be minimized.
Material Flow Properties
There are two major considerations for reliable flow; namely, cohesive strength and wall friction properties. Cohesive strength is measured using a bench scale laboratory testing device such as a direct shear tester (Jenike Shear Tester) seen here. This device is used to determine a material’s “Flow Function”, whereby the material’s cohesive strength is measured as a function of applied consolidation pressure (pressure/ strength relationship). The sample’s moisture content and particle size are controlled while the direct shear tester is capable of determining the effects of temperature and time of storage at rest. This information is then used to determine the opening size required to prevent arching and ratholing in a bin or hopper.
The Jenike Shear Tester is also used to measure wall friction properties. Consider that friction develop between a solid and the walls of a bin or hopper. Wall friction determines whether the solid will slide on the wall (mass flow) or adhere to the wall forcing it to flow preferentially on itself (funnel flow) rather than at the walls.
Additionally, the material’s compressibility (bulk density/pressure relationship) is determined. A Flow Report is created describing the material’s flow properties. This report indicates values to be used to design a new bin or modify and existing one. A Flow Report typically consists of the following:
Page 1: Title Page
The first page is obviously a title page with a description of the project, company, etc.
Pages 2 & 3: Introduction and General Comments
This contains a General Comments section and is meant to provide general information regarding the flowability of the particular material being tested. These comments are given without any bin geometry in mind and serve to help explain tabulated data in the following pages and how to interpret it.
Pages 4 & 5: Cohesive Properties Test Results
Section 1: Arching and Ratholing Dimensions of the Flow Report indicates the arching and ratholing dimensions of your material as a function of time at rest, temperature, etc, as follows:
Arching Dimensions–the following are indicated as conditions your material was exposed to:
Time at Rest, hrs—In the example report, the material was tested to simulate 0 hrs storage (continuous flow) or as if the material was put in a bin and flow initiated immediately, shown on page 4. As well, some period of storage at rest (shown further below) was simulated, such as overnight, 72 hr, etc.
Temp., ºF—The material was tested at 90 ºF for 0 hrs and at 90 ºF cooling to room temperature after 3 days at rest to simulate actual storage conditions.
Particle size—An estimate of the material’s particle size is given here just to indicate whether the material is coarse or fine. In this case it would be considered fairly fine as it is considered-10 mesh.
Moisture content—The material’s total moisture content was measured according to an ASTM standard.
P-Factor—P-Factor is an estimation of the effect of excess pressure on your material. The magnitude of the excess pressure or overpressure factor can be estimated for vibration and impact during charging into the bin as follows:
Vibrators can affect flow two ways as follows: (1) While vibrators are commonly used as flow aid devices, they also pack materials in bins and hoppers. It is recommended that a P-Factor of 1.5 be used to calculate arching dimensions when vibrators are in use. (2) Vibrators sometimes work well when your material gains strength with time but is easy handling during continuous flow (0 hrs storage). Vibrators should be used only to initiate flow and should be turned off once flow is initiated. The following equations can be used to estimate P-Factor due to vibrator use as described here:
P-Factor = (1 + x/g) or P-Factor = y/g, whichever is larger, where:
x = vertical upward component of acceleration y = horizontal component of acceleration
g = gravity constant
Impact on filling
If you are filling your bin with a material and it drops close to the outlet, the P-Factor should be calculated as follows:
P-FACTOR = (1 = m) [w/(A B γ)] 2h/g where:
w = weight flow rate into bin h = height of fall
m = 0 for a rectangular outlet m = 1 for a circular outlet
A = impact area
B = outlet size of cone or slot
γ = bulk density
Mass Flow Bc, ft—“B” is the hopper opening and “c” stands for conical, such that these dimensions are given for 0 hrs and for some period of storage at rest. These are the minimum arching dimensions for a conical hopper that is designed for mass flow.
Mass Flow Bp, ft—“B” again is the hopper opening, while “p” stands for planar or wedge type hoppers, such that these dimensions are given for 0 hrs and for some period of storage at rest. These are the minimum arching dimensions for the width of a slotted opening in a wedge hopper, designed for mass flow. Remember that the slot length should be at least three times the width.
Funnel Flow Bf, ft—“B” is the hopper opening and “f” stands for a funnel flow slotted opening, such that these dimensions are given for 0 hrs and for some period of storage at rest. These are the arching dimensions for a slotted opening in a funnel flow bin, such as a long slot on a flat bottom bin.
Time at Rest, hrs—Same as above
Temp., ºF—Same as above
σ1, psf—This is the major consolidation pressure acting on the material as it remains in a bin. This pressure is simulated in the laboratory tests.
EH, ft—Effective Head (EH) is determined as a result of material sliding on the cylinder walls. As it slides, the material loses some of its head pressure due to shear along the walls and is referred to as EH rather than the actual head of material. The effective head in the example report ranges from 5’ to 40’.
The critical rathole diameter DF is a function of the major consolidating pressure that acts on the solid in the bin, which is expressed in terms of EH, the effective consolidating head of solid in the bin, as follows:
EH = [R/(u k)] [ 1 – EXP(-uk H/R)]
R = hydraulic radius of the cylindrical portion of your bin, i.e. ratio of cross sectional area to circumference. R= D/4 for a circular cylinder of diameter D.
R = W/2 for a long rectangular cylinder of width W.
u= tan (PHI-PRIME), coefficient of friction between the stored solid and the cylinder walls
k= ratio of horizontal to vertical solids pressure. A value of 0.4 is usually acceptable within cylinders.
h= height of the cylindrical portion of a bin.
Critical Rathole Diameters, Df, ft—“D” is the diameter of the opening required to collapse a rathole, while “f” stands for funnel flow. If your effective is 20’ after 3 days at rest the rathole dimension is 18.3’, meaning that an 18.3’ diameter opening is required to collapse a rathole, even at this low head.
Page 6: Compressibility Test Results
Section 2 Bulk Density/Pressure Relationship of the Flow Report on Page 6 indicates the bulk density of your material as a function of consolidation pressure or head of material as follows:
EH, ft—Same as above
γ, pcf—γ is the Greek symbol used for bulk density. There are a range of bulk densities when dealing with solids, not just loose density and packed density. In this case, γ ranges from 38.2 pcf to 48.9 pcf. γ is used in opening size and hopper angle calculations along with bin and feeder load calculations.
Page 7: Wall Friction Properties Test Results
Section 3 Recommended Hopper Angles for Mass Flow of the Flow Report beginning on Page 7, indicates the conical and wedge hopper angles required to ensure flow along the walls i.e. mass flow, as follows:
Outlet Dia., Cone, ft – Is usually interpreted as the conical opening size; however, it could be any span in the hopper, not just the opening.
Outlet Width, Slot, ft – Is usually interpreted as the slot opening size; however, it could be any span in the hopper, not just the opening.
ø’ – This is the wall friction angle generated during a wall friction on a particular wall surface. It is given in degrees from horizontal.
θc – This is the hopper angle (degrees from vertical) required for mass flow in a conical hopper.
θp – This is the hopper (degrees from vertical) required for mass flow along the sidewall of a wedge type hopper.
As an example of using these dimensions, you could design a mass flow conical hopper with a 2.1’ diameter opening (to prevent arching) or a slot that is 1.0 ft wide, that would require the following hopper slopes (depending on the wall surface preferred):
Wall Surface θc θp
2B stainless steel 16 27
TIVAR 88 23 33
Carbon steel 7 16
To summarize, the Flow Report essentially describes the geometry required to ensure reliable flow. It yields opening sizes to prevent arching and ratholing, bulk density values, and hopper angles required for mass flow.